At first let's examine results that are produced by famous centralized solutions. We don't provide any mechanism here but we are trying to impose the cost sharing which satisfy some basic requirements such as pareto-optimality. 

For no mechanism exists, the Central Planner doesn't ask agents any information about their preferences. The only thing she collects is the endowment of the agents (households) and the suposition how much the agents need the enhancement of security system. The former can be represented by the household income or the size of the dwelling. The latter can be obtained from the statistics about lawbreaking in the particular area or just represent the percentage of under-age members of the household. The actual meaning of these figures are of low importance within this study; more significant is the statement that the reliable utility function can be obtained without any (or very limited) communication with the agents so the free-rider problem vanishes.

Within this section we shall investigate the solutions yielded by four famous centralized solutions, namely: Mill's utilitarian solution, Rawls' egalitarian solution, Nash's bargaining solution and its adversary - Kalai-Smorodinsky bargaining solution. Every subsection devoted to the particular method shall have the same structure. After proposal of the mathematical model we'll introduce the AMPL program code, succeeded by the results and charts. 

In order to compare the solutions we'll introduce several evaluation methods such as Lorenz curves along with Gini index and also Theil index and Hoover index. The novelty lies in using those inequality metrics for evaluating utility allocations.

The solutions will be followed by the discussion over the results and applied comparison approaches. Beforehand we shall look at the generated scenarios.


